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A game which is played by the following rules. Given one or more piles (nim-heaps), players alternate by taking all or some of the counters in a single heap. The player ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

A surface such as the Möbius strip or Klein bottle (Gray 1997, pp. 322-323) on which there exists a closed path such that the directrix is reversed when moved around this ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

The outer Napoleon triangle is the triangle DeltaN_C^'N_B^'N_A^' formed by the centers of externally erected equilateral triangles DeltaABE_C^', DeltaACE_B^', and ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...

The term "pathological" is used in mathematics to refer to an example specifically cooked up to violate certain almost universally valid properties. Pathological problems ...

The answer to the question "which fits better, a round peg in a square hole, or a square peg in a round hole?" can be interpreted as asking which is larger, the ratio of the ...

A pentagonal square triangular number is a number that is simultaneously a pentagonal number P_l, a square number S_m, and a triangular number T_n. This requires a solution ...

Let x:U->R^3 be a regular patch, where U is an open subset of R^2. Then (partiale)/(partialv)-(partialf)/(partialu) = eGamma_(12)^1+f(Gamma_(12)^2-Gamma_(11)^1)-gGamma_(11)^2 ...